# Properties

 Label 630.2.bk.a.101.1 Level 630 Weight 2 Character 630.101 Analytic conductor 5.031 Analytic rank 1 Dimension 4 CM no Inner twists 2

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$630 = 2 \cdot 3^{2} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 630.bk (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$5.03057532734$$ Analytic rank: $$1$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 101.1 Root $$0.866025 - 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 630.101 Dual form 630.2.bk.a.131.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000i q^{2} +(0.866025 - 1.50000i) q^{3} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(-2.50000 + 0.866025i) q^{7} +1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$$ $$q-1.00000i q^{2} +(0.866025 - 1.50000i) q^{3} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(-2.50000 + 0.866025i) q^{7} +1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +(0.866025 + 0.500000i) q^{10} +(-4.09808 + 2.36603i) q^{11} +(-0.866025 + 1.50000i) q^{12} +(-3.00000 + 1.73205i) q^{13} +(0.866025 + 2.50000i) q^{14} +(0.866025 + 1.50000i) q^{15} +1.00000 q^{16} +(-2.59808 + 1.50000i) q^{18} +(-1.09808 + 0.633975i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-0.866025 + 4.50000i) q^{21} +(2.36603 + 4.09808i) q^{22} +(2.19615 + 1.26795i) q^{23} +(1.50000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(1.73205 + 3.00000i) q^{26} -5.19615 q^{27} +(2.50000 - 0.866025i) q^{28} +(-5.59808 - 3.23205i) q^{29} +(1.50000 - 0.866025i) q^{30} -8.19615i q^{31} -1.00000i q^{32} +8.19615i q^{33} +(0.500000 - 2.59808i) q^{35} +(1.50000 + 2.59808i) q^{36} +(-3.09808 - 5.36603i) q^{37} +(0.633975 + 1.09808i) q^{38} +6.00000i q^{39} +(-0.866025 - 0.500000i) q^{40} +(4.50000 + 7.79423i) q^{41} +(4.50000 + 0.866025i) q^{42} +(-1.59808 + 2.76795i) q^{43} +(4.09808 - 2.36603i) q^{44} +3.00000 q^{45} +(1.26795 - 2.19615i) q^{46} -9.00000 q^{47} +(0.866025 - 1.50000i) q^{48} +(5.50000 - 4.33013i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(3.00000 - 1.73205i) q^{52} +(6.29423 + 3.63397i) q^{53} +5.19615i q^{54} -4.73205i q^{55} +(-0.866025 - 2.50000i) q^{56} +2.19615i q^{57} +(-3.23205 + 5.59808i) q^{58} +2.19615 q^{59} +(-0.866025 - 1.50000i) q^{60} -12.9282i q^{61} -8.19615 q^{62} +(6.00000 + 5.19615i) q^{63} -1.00000 q^{64} -3.46410i q^{65} +8.19615 q^{66} -4.00000 q^{67} +(3.80385 - 2.19615i) q^{69} +(-2.59808 - 0.500000i) q^{70} +4.73205i q^{71} +(2.59808 - 1.50000i) q^{72} +(6.00000 + 3.46410i) q^{73} +(-5.36603 + 3.09808i) q^{74} -1.73205 q^{75} +(1.09808 - 0.633975i) q^{76} +(8.19615 - 9.46410i) q^{77} +6.00000 q^{78} +14.5885 q^{79} +(-0.500000 + 0.866025i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(7.79423 - 4.50000i) q^{82} +(-5.59808 + 9.69615i) q^{83} +(0.866025 - 4.50000i) q^{84} +(2.76795 + 1.59808i) q^{86} +(-9.69615 + 5.59808i) q^{87} +(-2.36603 - 4.09808i) q^{88} +(2.19615 + 3.80385i) q^{89} -3.00000i q^{90} +(6.00000 - 6.92820i) q^{91} +(-2.19615 - 1.26795i) q^{92} +(-12.2942 - 7.09808i) q^{93} +9.00000i q^{94} -1.26795i q^{95} +(-1.50000 - 0.866025i) q^{96} +(-7.39230 - 4.26795i) q^{97} +(-4.33013 - 5.50000i) q^{98} +(12.2942 + 7.09808i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q - 4q^{4} - 2q^{5} - 6q^{6} - 10q^{7} - 6q^{9} + O(q^{10})$$ $$4q - 4q^{4} - 2q^{5} - 6q^{6} - 10q^{7} - 6q^{9} - 6q^{11} - 12q^{13} + 4q^{16} + 6q^{19} + 2q^{20} + 6q^{22} - 12q^{23} + 6q^{24} - 2q^{25} + 10q^{28} - 12q^{29} + 6q^{30} + 2q^{35} + 6q^{36} - 2q^{37} + 6q^{38} + 18q^{41} + 18q^{42} + 4q^{43} + 6q^{44} + 12q^{45} + 12q^{46} - 36q^{47} + 22q^{49} + 12q^{52} - 6q^{53} - 6q^{58} - 12q^{59} - 12q^{62} + 24q^{63} - 4q^{64} + 12q^{66} - 16q^{67} + 36q^{69} + 24q^{73} - 18q^{74} - 6q^{76} + 12q^{77} + 24q^{78} - 4q^{79} - 2q^{80} - 18q^{81} - 12q^{83} + 18q^{86} - 18q^{87} - 6q^{88} - 12q^{89} + 24q^{91} + 12q^{92} - 18q^{93} - 6q^{96} + 12q^{97} + 18q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$281$$ $$451$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000i 0.707107i
$$3$$ 0.866025 1.50000i 0.500000 0.866025i
$$4$$ −1.00000 −0.500000
$$5$$ −0.500000 + 0.866025i −0.223607 + 0.387298i
$$6$$ −1.50000 0.866025i −0.612372 0.353553i
$$7$$ −2.50000 + 0.866025i −0.944911 + 0.327327i
$$8$$ 1.00000i 0.353553i
$$9$$ −1.50000 2.59808i −0.500000 0.866025i
$$10$$ 0.866025 + 0.500000i 0.273861 + 0.158114i
$$11$$ −4.09808 + 2.36603i −1.23562 + 0.713384i −0.968195 0.250196i $$-0.919505\pi$$
−0.267421 + 0.963580i $$0.586172\pi$$
$$12$$ −0.866025 + 1.50000i −0.250000 + 0.433013i
$$13$$ −3.00000 + 1.73205i −0.832050 + 0.480384i −0.854554 0.519362i $$-0.826170\pi$$
0.0225039 + 0.999747i $$0.492836\pi$$
$$14$$ 0.866025 + 2.50000i 0.231455 + 0.668153i
$$15$$ 0.866025 + 1.50000i 0.223607 + 0.387298i
$$16$$ 1.00000 0.250000
$$17$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$18$$ −2.59808 + 1.50000i −0.612372 + 0.353553i
$$19$$ −1.09808 + 0.633975i −0.251916 + 0.145444i −0.620641 0.784095i $$-0.713128\pi$$
0.368725 + 0.929538i $$0.379794\pi$$
$$20$$ 0.500000 0.866025i 0.111803 0.193649i
$$21$$ −0.866025 + 4.50000i −0.188982 + 0.981981i
$$22$$ 2.36603 + 4.09808i 0.504438 + 0.873713i
$$23$$ 2.19615 + 1.26795i 0.457929 + 0.264386i 0.711173 0.703017i $$-0.248164\pi$$
−0.253244 + 0.967402i $$0.581497\pi$$
$$24$$ 1.50000 + 0.866025i 0.306186 + 0.176777i
$$25$$ −0.500000 0.866025i −0.100000 0.173205i
$$26$$ 1.73205 + 3.00000i 0.339683 + 0.588348i
$$27$$ −5.19615 −1.00000
$$28$$ 2.50000 0.866025i 0.472456 0.163663i
$$29$$ −5.59808 3.23205i −1.03954 0.600177i −0.119835 0.992794i $$-0.538236\pi$$
−0.919702 + 0.392617i $$0.871570\pi$$
$$30$$ 1.50000 0.866025i 0.273861 0.158114i
$$31$$ 8.19615i 1.47207i −0.676942 0.736036i $$-0.736695\pi$$
0.676942 0.736036i $$-0.263305\pi$$
$$32$$ 1.00000i 0.176777i
$$33$$ 8.19615i 1.42677i
$$34$$ 0 0
$$35$$ 0.500000 2.59808i 0.0845154 0.439155i
$$36$$ 1.50000 + 2.59808i 0.250000 + 0.433013i
$$37$$ −3.09808 5.36603i −0.509321 0.882169i −0.999942 0.0107961i $$-0.996563\pi$$
0.490621 0.871373i $$-0.336770\pi$$
$$38$$ 0.633975 + 1.09808i 0.102844 + 0.178131i
$$39$$ 6.00000i 0.960769i
$$40$$ −0.866025 0.500000i −0.136931 0.0790569i
$$41$$ 4.50000 + 7.79423i 0.702782 + 1.21725i 0.967486 + 0.252924i $$0.0813924\pi$$
−0.264704 + 0.964330i $$0.585274\pi$$
$$42$$ 4.50000 + 0.866025i 0.694365 + 0.133631i
$$43$$ −1.59808 + 2.76795i −0.243704 + 0.422108i −0.961767 0.273871i $$-0.911696\pi$$
0.718062 + 0.695979i $$0.245029\pi$$
$$44$$ 4.09808 2.36603i 0.617808 0.356692i
$$45$$ 3.00000 0.447214
$$46$$ 1.26795 2.19615i 0.186949 0.323805i
$$47$$ −9.00000 −1.31278 −0.656392 0.754420i $$-0.727918\pi$$
−0.656392 + 0.754420i $$0.727918\pi$$
$$48$$ 0.866025 1.50000i 0.125000 0.216506i
$$49$$ 5.50000 4.33013i 0.785714 0.618590i
$$50$$ −0.866025 + 0.500000i −0.122474 + 0.0707107i
$$51$$ 0 0
$$52$$ 3.00000 1.73205i 0.416025 0.240192i
$$53$$ 6.29423 + 3.63397i 0.864579 + 0.499165i 0.865543 0.500835i $$-0.166974\pi$$
−0.000964138 1.00000i $$0.500307\pi$$
$$54$$ 5.19615i 0.707107i
$$55$$ 4.73205i 0.638070i
$$56$$ −0.866025 2.50000i −0.115728 0.334077i
$$57$$ 2.19615i 0.290887i
$$58$$ −3.23205 + 5.59808i −0.424389 + 0.735063i
$$59$$ 2.19615 0.285915 0.142957 0.989729i $$-0.454339\pi$$
0.142957 + 0.989729i $$0.454339\pi$$
$$60$$ −0.866025 1.50000i −0.111803 0.193649i
$$61$$ 12.9282i 1.65529i −0.561254 0.827643i $$-0.689681\pi$$
0.561254 0.827643i $$-0.310319\pi$$
$$62$$ −8.19615 −1.04091
$$63$$ 6.00000 + 5.19615i 0.755929 + 0.654654i
$$64$$ −1.00000 −0.125000
$$65$$ 3.46410i 0.429669i
$$66$$ 8.19615 1.00888
$$67$$ −4.00000 −0.488678 −0.244339 0.969690i $$-0.578571\pi$$
−0.244339 + 0.969690i $$0.578571\pi$$
$$68$$ 0 0
$$69$$ 3.80385 2.19615i 0.457929 0.264386i
$$70$$ −2.59808 0.500000i −0.310530 0.0597614i
$$71$$ 4.73205i 0.561591i 0.959768 + 0.280796i $$0.0905983\pi$$
−0.959768 + 0.280796i $$0.909402\pi$$
$$72$$ 2.59808 1.50000i 0.306186 0.176777i
$$73$$ 6.00000 + 3.46410i 0.702247 + 0.405442i 0.808184 0.588930i $$-0.200451\pi$$
−0.105937 + 0.994373i $$0.533784\pi$$
$$74$$ −5.36603 + 3.09808i −0.623788 + 0.360144i
$$75$$ −1.73205 −0.200000
$$76$$ 1.09808 0.633975i 0.125958 0.0727219i
$$77$$ 8.19615 9.46410i 0.934038 1.07853i
$$78$$ 6.00000 0.679366
$$79$$ 14.5885 1.64133 0.820665 0.571410i $$-0.193603\pi$$
0.820665 + 0.571410i $$0.193603\pi$$
$$80$$ −0.500000 + 0.866025i −0.0559017 + 0.0968246i
$$81$$ −4.50000 + 7.79423i −0.500000 + 0.866025i
$$82$$ 7.79423 4.50000i 0.860729 0.496942i
$$83$$ −5.59808 + 9.69615i −0.614469 + 1.06429i 0.376009 + 0.926616i $$0.377296\pi$$
−0.990477 + 0.137675i $$0.956037\pi$$
$$84$$ 0.866025 4.50000i 0.0944911 0.490990i
$$85$$ 0 0
$$86$$ 2.76795 + 1.59808i 0.298476 + 0.172325i
$$87$$ −9.69615 + 5.59808i −1.03954 + 0.600177i
$$88$$ −2.36603 4.09808i −0.252219 0.436856i
$$89$$ 2.19615 + 3.80385i 0.232792 + 0.403207i 0.958629 0.284660i $$-0.0918806\pi$$
−0.725837 + 0.687867i $$0.758547\pi$$
$$90$$ 3.00000i 0.316228i
$$91$$ 6.00000 6.92820i 0.628971 0.726273i
$$92$$ −2.19615 1.26795i −0.228965 0.132193i
$$93$$ −12.2942 7.09808i −1.27485 0.736036i
$$94$$ 9.00000i 0.928279i
$$95$$ 1.26795i 0.130089i
$$96$$ −1.50000 0.866025i −0.153093 0.0883883i
$$97$$ −7.39230 4.26795i −0.750575 0.433345i 0.0753267 0.997159i $$-0.476000\pi$$
−0.825902 + 0.563814i $$0.809333\pi$$
$$98$$ −4.33013 5.50000i −0.437409 0.555584i
$$99$$ 12.2942 + 7.09808i 1.23562 + 0.713384i
$$100$$ 0.500000 + 0.866025i 0.0500000 + 0.0866025i
$$101$$ −5.59808 9.69615i −0.557029 0.964803i −0.997743 0.0671552i $$-0.978608\pi$$
0.440713 0.897648i $$-0.354726\pi$$
$$102$$ 0 0
$$103$$ −10.5000 6.06218i −1.03460 0.597324i −0.116298 0.993214i $$-0.537103\pi$$
−0.918298 + 0.395890i $$0.870436\pi$$
$$104$$ −1.73205 3.00000i −0.169842 0.294174i
$$105$$ −3.46410 3.00000i −0.338062 0.292770i
$$106$$ 3.63397 6.29423i 0.352963 0.611350i
$$107$$ −13.7942 + 7.96410i −1.33354 + 0.769919i −0.985840 0.167688i $$-0.946370\pi$$
−0.347698 + 0.937606i $$0.613037\pi$$
$$108$$ 5.19615 0.500000
$$109$$ 3.59808 6.23205i 0.344633 0.596922i −0.640654 0.767830i $$-0.721337\pi$$
0.985287 + 0.170908i $$0.0546700\pi$$
$$110$$ −4.73205 −0.451183
$$111$$ −10.7321 −1.01864
$$112$$ −2.50000 + 0.866025i −0.236228 + 0.0818317i
$$113$$ −10.9019 + 6.29423i −1.02557 + 0.592111i −0.915711 0.401836i $$-0.868372\pi$$
−0.109855 + 0.993948i $$0.535039\pi$$
$$114$$ 2.19615 0.205689
$$115$$ −2.19615 + 1.26795i −0.204792 + 0.118237i
$$116$$ 5.59808 + 3.23205i 0.519768 + 0.300088i
$$117$$ 9.00000 + 5.19615i 0.832050 + 0.480384i
$$118$$ 2.19615i 0.202172i
$$119$$ 0 0
$$120$$ −1.50000 + 0.866025i −0.136931 + 0.0790569i
$$121$$ 5.69615 9.86603i 0.517832 0.896911i
$$122$$ −12.9282 −1.17046
$$123$$ 15.5885 1.40556
$$124$$ 8.19615i 0.736036i
$$125$$ 1.00000 0.0894427
$$126$$ 5.19615 6.00000i 0.462910 0.534522i
$$127$$ −11.3923 −1.01090 −0.505452 0.862855i $$-0.668674\pi$$
−0.505452 + 0.862855i $$0.668674\pi$$
$$128$$ 1.00000i 0.0883883i
$$129$$ 2.76795 + 4.79423i 0.243704 + 0.422108i
$$130$$ −3.46410 −0.303822
$$131$$ 2.19615 3.80385i 0.191879 0.332344i −0.753994 0.656881i $$-0.771875\pi$$
0.945873 + 0.324537i $$0.105209\pi$$
$$132$$ 8.19615i 0.713384i
$$133$$ 2.19615 2.53590i 0.190431 0.219890i
$$134$$ 4.00000i 0.345547i
$$135$$ 2.59808 4.50000i 0.223607 0.387298i
$$136$$ 0 0
$$137$$ 6.29423 3.63397i 0.537752 0.310471i −0.206415 0.978464i $$-0.566180\pi$$
0.744167 + 0.667993i $$0.232846\pi$$
$$138$$ −2.19615 3.80385i −0.186949 0.323805i
$$139$$ −19.0981 + 11.0263i −1.61988 + 0.935237i −0.632927 + 0.774211i $$0.718147\pi$$
−0.986950 + 0.161026i $$0.948520\pi$$
$$140$$ −0.500000 + 2.59808i −0.0422577 + 0.219578i
$$141$$ −7.79423 + 13.5000i −0.656392 + 1.13691i
$$142$$ 4.73205 0.397105
$$143$$ 8.19615 14.1962i 0.685397 1.18714i
$$144$$ −1.50000 2.59808i −0.125000 0.216506i
$$145$$ 5.59808 3.23205i 0.464895 0.268407i
$$146$$ 3.46410 6.00000i 0.286691 0.496564i
$$147$$ −1.73205 12.0000i −0.142857 0.989743i
$$148$$ 3.09808 + 5.36603i 0.254660 + 0.441085i
$$149$$ 10.3923 + 6.00000i 0.851371 + 0.491539i 0.861113 0.508413i $$-0.169768\pi$$
−0.00974235 + 0.999953i $$0.503101\pi$$
$$150$$ 1.73205i 0.141421i
$$151$$ 2.09808 + 3.63397i 0.170739 + 0.295729i 0.938678 0.344794i $$-0.112051\pi$$
−0.767939 + 0.640522i $$0.778718\pi$$
$$152$$ −0.633975 1.09808i −0.0514221 0.0890657i
$$153$$ 0 0
$$154$$ −9.46410 8.19615i −0.762639 0.660465i
$$155$$ 7.09808 + 4.09808i 0.570131 + 0.329165i
$$156$$ 6.00000i 0.480384i
$$157$$ 17.6603i 1.40944i −0.709485 0.704721i $$-0.751072\pi$$
0.709485 0.704721i $$-0.248928\pi$$
$$158$$ 14.5885i 1.16060i
$$159$$ 10.9019 6.29423i 0.864579 0.499165i
$$160$$ 0.866025 + 0.500000i 0.0684653 + 0.0395285i
$$161$$ −6.58846 1.26795i −0.519243 0.0999284i
$$162$$ 7.79423 + 4.50000i 0.612372 + 0.353553i
$$163$$ 4.19615 + 7.26795i 0.328668 + 0.569270i 0.982248 0.187588i $$-0.0600669\pi$$
−0.653580 + 0.756858i $$0.726734\pi$$
$$164$$ −4.50000 7.79423i −0.351391 0.608627i
$$165$$ −7.09808 4.09808i −0.552584 0.319035i
$$166$$ 9.69615 + 5.59808i 0.752567 + 0.434495i
$$167$$ −5.19615 9.00000i −0.402090 0.696441i 0.591888 0.806020i $$-0.298383\pi$$
−0.993978 + 0.109580i $$0.965050\pi$$
$$168$$ −4.50000 0.866025i −0.347183 0.0668153i
$$169$$ −0.500000 + 0.866025i −0.0384615 + 0.0666173i
$$170$$ 0 0
$$171$$ 3.29423 + 1.90192i 0.251916 + 0.145444i
$$172$$ 1.59808 2.76795i 0.121852 0.211054i
$$173$$ 8.19615 0.623142 0.311571 0.950223i $$-0.399145\pi$$
0.311571 + 0.950223i $$0.399145\pi$$
$$174$$ 5.59808 + 9.69615i 0.424389 + 0.735063i
$$175$$ 2.00000 + 1.73205i 0.151186 + 0.130931i
$$176$$ −4.09808 + 2.36603i −0.308904 + 0.178346i
$$177$$ 1.90192 3.29423i 0.142957 0.247609i
$$178$$ 3.80385 2.19615i 0.285110 0.164609i
$$179$$ −21.2942 12.2942i −1.59161 0.918914i −0.993032 0.117846i $$-0.962401\pi$$
−0.598573 0.801068i $$-0.704266\pi$$
$$180$$ −3.00000 −0.223607
$$181$$ 13.3923i 0.995442i −0.867337 0.497721i $$-0.834170\pi$$
0.867337 0.497721i $$-0.165830\pi$$
$$182$$ −6.92820 6.00000i −0.513553 0.444750i
$$183$$ −19.3923 11.1962i −1.43352 0.827643i
$$184$$ −1.26795 + 2.19615i −0.0934745 + 0.161903i
$$185$$ 6.19615 0.455550
$$186$$ −7.09808 + 12.2942i −0.520456 + 0.901457i
$$187$$ 0 0
$$188$$ 9.00000 0.656392
$$189$$ 12.9904 4.50000i 0.944911 0.327327i
$$190$$ −1.26795 −0.0919867
$$191$$ 3.46410i 0.250654i 0.992116 + 0.125327i $$0.0399979\pi$$
−0.992116 + 0.125327i $$0.960002\pi$$
$$192$$ −0.866025 + 1.50000i −0.0625000 + 0.108253i
$$193$$ 13.8038 0.993623 0.496811 0.867859i $$-0.334504\pi$$
0.496811 + 0.867859i $$0.334504\pi$$
$$194$$ −4.26795 + 7.39230i −0.306421 + 0.530737i
$$195$$ −5.19615 3.00000i −0.372104 0.214834i
$$196$$ −5.50000 + 4.33013i −0.392857 + 0.309295i
$$197$$ 23.6603i 1.68572i 0.538130 + 0.842862i $$0.319131\pi$$
−0.538130 + 0.842862i $$0.680869\pi$$
$$198$$ 7.09808 12.2942i 0.504438 0.873713i
$$199$$ 6.00000 + 3.46410i 0.425329 + 0.245564i 0.697355 0.716726i $$-0.254360\pi$$
−0.272026 + 0.962290i $$0.587694\pi$$
$$200$$ 0.866025 0.500000i 0.0612372 0.0353553i
$$201$$ −3.46410 + 6.00000i −0.244339 + 0.423207i
$$202$$ −9.69615 + 5.59808i −0.682219 + 0.393879i
$$203$$ 16.7942 + 3.23205i 1.17872 + 0.226845i
$$204$$ 0 0
$$205$$ −9.00000 −0.628587
$$206$$ −6.06218 + 10.5000i −0.422372 + 0.731570i
$$207$$ 7.60770i 0.528771i
$$208$$ −3.00000 + 1.73205i −0.208013 + 0.120096i
$$209$$ 3.00000 5.19615i 0.207514 0.359425i
$$210$$ −3.00000 + 3.46410i −0.207020 + 0.239046i
$$211$$ 10.2942 + 17.8301i 0.708684 + 1.22748i 0.965345 + 0.260975i $$0.0840441\pi$$
−0.256662 + 0.966501i $$0.582623\pi$$
$$212$$ −6.29423 3.63397i −0.432289 0.249582i
$$213$$ 7.09808 + 4.09808i 0.486352 + 0.280796i
$$214$$ 7.96410 + 13.7942i 0.544415 + 0.942954i
$$215$$ −1.59808 2.76795i −0.108988 0.188773i
$$216$$ 5.19615i 0.353553i
$$217$$ 7.09808 + 20.4904i 0.481849 + 1.39098i
$$218$$ −6.23205 3.59808i −0.422088 0.243692i
$$219$$ 10.3923 6.00000i 0.702247 0.405442i
$$220$$ 4.73205i 0.319035i
$$221$$ 0 0
$$222$$ 10.7321i 0.720288i
$$223$$ −11.8923 6.86603i −0.796368 0.459783i 0.0458318 0.998949i $$-0.485406\pi$$
−0.842199 + 0.539166i $$0.818740\pi$$
$$224$$ 0.866025 + 2.50000i 0.0578638 + 0.167038i
$$225$$ −1.50000 + 2.59808i −0.100000 + 0.173205i
$$226$$ 6.29423 + 10.9019i 0.418686 + 0.725185i
$$227$$ −8.19615 14.1962i −0.543998 0.942232i −0.998669 0.0515725i $$-0.983577\pi$$
0.454672 0.890659i $$-0.349757\pi$$
$$228$$ 2.19615i 0.145444i
$$229$$ −12.1865 7.03590i −0.805309 0.464945i 0.0400153 0.999199i $$-0.487259\pi$$
−0.845324 + 0.534254i $$0.820593\pi$$
$$230$$ 1.26795 + 2.19615i 0.0836061 + 0.144810i
$$231$$ −7.09808 20.4904i −0.467019 1.34817i
$$232$$ 3.23205 5.59808i 0.212195 0.367532i
$$233$$ −1.09808 + 0.633975i −0.0719374 + 0.0415331i −0.535537 0.844512i $$-0.679891\pi$$
0.463600 + 0.886045i $$0.346558\pi$$
$$234$$ 5.19615 9.00000i 0.339683 0.588348i
$$235$$ 4.50000 7.79423i 0.293548 0.508439i
$$236$$ −2.19615 −0.142957
$$237$$ 12.6340 21.8827i 0.820665 1.42143i
$$238$$ 0 0
$$239$$ 2.70577 1.56218i 0.175022 0.101049i −0.409930 0.912117i $$-0.634447\pi$$
0.584952 + 0.811068i $$0.301113\pi$$
$$240$$ 0.866025 + 1.50000i 0.0559017 + 0.0968246i
$$241$$ 2.89230 1.66987i 0.186310 0.107566i −0.403944 0.914784i $$-0.632361\pi$$
0.590254 + 0.807218i $$0.299028\pi$$
$$242$$ −9.86603 5.69615i −0.634212 0.366163i
$$243$$ 7.79423 + 13.5000i 0.500000 + 0.866025i
$$244$$ 12.9282i 0.827643i
$$245$$ 1.00000 + 6.92820i 0.0638877 + 0.442627i
$$246$$ 15.5885i 0.993884i
$$247$$ 2.19615 3.80385i 0.139738 0.242033i
$$248$$ 8.19615 0.520456
$$249$$ 9.69615 + 16.7942i 0.614469 + 1.06429i
$$250$$ 1.00000i 0.0632456i
$$251$$ 18.0000 1.13615 0.568075 0.822977i $$-0.307688\pi$$
0.568075 + 0.822977i $$0.307688\pi$$
$$252$$ −6.00000 5.19615i −0.377964 0.327327i
$$253$$ −12.0000 −0.754434
$$254$$ 11.3923i 0.714817i
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 14.1962 24.5885i 0.885532 1.53379i 0.0404286 0.999182i $$-0.487128\pi$$
0.845103 0.534603i $$-0.179539\pi$$
$$258$$ 4.79423 2.76795i 0.298476 0.172325i
$$259$$ 12.3923 + 10.7321i 0.770020 + 0.666857i
$$260$$ 3.46410i 0.214834i
$$261$$ 19.3923i 1.20035i
$$262$$ −3.80385 2.19615i −0.235002 0.135679i
$$263$$ −11.8923 + 6.86603i −0.733311 + 0.423377i −0.819632 0.572890i $$-0.805822\pi$$
0.0863213 + 0.996267i $$0.472489\pi$$
$$264$$ −8.19615 −0.504438
$$265$$ −6.29423 + 3.63397i −0.386651 + 0.223233i
$$266$$ −2.53590 2.19615i −0.155486 0.134655i
$$267$$ 7.60770 0.465583
$$268$$ 4.00000 0.244339
$$269$$ −9.00000 + 15.5885i −0.548740 + 0.950445i 0.449622 + 0.893219i $$0.351559\pi$$
−0.998361 + 0.0572259i $$0.981774\pi$$
$$270$$ −4.50000 2.59808i −0.273861 0.158114i
$$271$$ 5.70577 3.29423i 0.346601 0.200110i −0.316586 0.948564i $$-0.602537\pi$$
0.663187 + 0.748454i $$0.269203\pi$$
$$272$$ 0 0
$$273$$ −5.19615 15.0000i −0.314485 0.907841i
$$274$$ −3.63397 6.29423i −0.219536 0.380248i
$$275$$ 4.09808 + 2.36603i 0.247123 + 0.142677i
$$276$$ −3.80385 + 2.19615i −0.228965 + 0.132193i
$$277$$ 12.0981 + 20.9545i 0.726903 + 1.25903i 0.958186 + 0.286146i $$0.0923743\pi$$
−0.231283 + 0.972887i $$0.574292\pi$$
$$278$$ 11.0263 + 19.0981i 0.661312 + 1.14543i
$$279$$ −21.2942 + 12.2942i −1.27485 + 0.736036i
$$280$$ 2.59808 + 0.500000i 0.155265 + 0.0298807i
$$281$$ 12.6962 + 7.33013i 0.757389 + 0.437279i 0.828357 0.560200i $$-0.189276\pi$$
−0.0709685 + 0.997479i $$0.522609\pi$$
$$282$$ 13.5000 + 7.79423i 0.803913 + 0.464140i
$$283$$ 16.8564i 1.00201i −0.865445 0.501005i $$-0.832964\pi$$
0.865445 0.501005i $$-0.167036\pi$$
$$284$$ 4.73205i 0.280796i
$$285$$ −1.90192 1.09808i −0.112660 0.0650444i
$$286$$ −14.1962 8.19615i −0.839436 0.484649i
$$287$$ −18.0000 15.5885i −1.06251 0.920158i
$$288$$ −2.59808 + 1.50000i −0.153093 + 0.0883883i
$$289$$ 8.50000 + 14.7224i 0.500000 + 0.866025i
$$290$$ −3.23205 5.59808i −0.189793 0.328730i
$$291$$ −12.8038 + 7.39230i −0.750575 + 0.433345i
$$292$$ −6.00000 3.46410i −0.351123 0.202721i
$$293$$ 8.19615 + 14.1962i 0.478824 + 0.829348i 0.999705 0.0242813i $$-0.00772975\pi$$
−0.520881 + 0.853629i $$0.674396\pi$$
$$294$$ −12.0000 + 1.73205i −0.699854 + 0.101015i
$$295$$ −1.09808 + 1.90192i −0.0639325 + 0.110734i
$$296$$ 5.36603 3.09808i 0.311894 0.180072i
$$297$$ 21.2942 12.2942i 1.23562 0.713384i
$$298$$ 6.00000 10.3923i 0.347571 0.602010i
$$299$$ −8.78461 −0.508027
$$300$$ 1.73205 0.100000
$$301$$ 1.59808 8.30385i 0.0921116 0.478626i
$$302$$ 3.63397 2.09808i 0.209112 0.120731i
$$303$$ −19.3923 −1.11406
$$304$$ −1.09808 + 0.633975i −0.0629790 + 0.0363609i
$$305$$ 11.1962 + 6.46410i 0.641090 + 0.370133i
$$306$$ 0 0
$$307$$ 23.7846i 1.35746i 0.734388 + 0.678730i $$0.237469\pi$$
−0.734388 + 0.678730i $$0.762531\pi$$
$$308$$ −8.19615 + 9.46410i −0.467019 + 0.539267i
$$309$$ −18.1865 + 10.5000i −1.03460 + 0.597324i
$$310$$ 4.09808 7.09808i 0.232755 0.403144i
$$311$$ −15.8038 −0.896154 −0.448077 0.893995i $$-0.647891\pi$$
−0.448077 + 0.893995i $$0.647891\pi$$
$$312$$ −6.00000 −0.339683
$$313$$ 20.1962i 1.14155i 0.821105 + 0.570777i $$0.193358\pi$$
−0.821105 + 0.570777i $$0.806642\pi$$
$$314$$ −17.6603 −0.996626
$$315$$ −7.50000 + 2.59808i −0.422577 + 0.146385i
$$316$$ −14.5885 −0.820665
$$317$$ 20.5359i 1.15341i 0.816952 + 0.576705i $$0.195662\pi$$
−0.816952 + 0.576705i $$0.804338\pi$$
$$318$$ −6.29423 10.9019i −0.352963 0.611350i
$$319$$ 30.5885 1.71262
$$320$$ 0.500000 0.866025i 0.0279508 0.0484123i
$$321$$ 27.5885i 1.53984i
$$322$$ −1.26795 + 6.58846i −0.0706600 + 0.367160i
$$323$$ 0 0
$$324$$ 4.50000 7.79423i 0.250000 0.433013i
$$325$$ 3.00000 + 1.73205i 0.166410 + 0.0960769i
$$326$$ 7.26795 4.19615i 0.402534 0.232403i
$$327$$ −6.23205 10.7942i −0.344633 0.596922i
$$328$$ −7.79423 + 4.50000i −0.430364 + 0.248471i
$$329$$ 22.5000 7.79423i 1.24047 0.429710i
$$330$$ −4.09808 + 7.09808i −0.225592 + 0.390736i
$$331$$ −8.00000 −0.439720 −0.219860 0.975531i $$-0.570560\pi$$
−0.219860 + 0.975531i $$0.570560\pi$$
$$332$$ 5.59808 9.69615i 0.307234 0.532145i
$$333$$ −9.29423 + 16.0981i −0.509321 + 0.882169i
$$334$$ −9.00000 + 5.19615i −0.492458 + 0.284321i
$$335$$ 2.00000 3.46410i 0.109272 0.189264i
$$336$$ −0.866025 + 4.50000i −0.0472456 + 0.245495i
$$337$$ −5.00000 8.66025i −0.272367 0.471754i 0.697100 0.716974i $$-0.254473\pi$$
−0.969468 + 0.245220i $$0.921140\pi$$
$$338$$ 0.866025 + 0.500000i 0.0471056 + 0.0271964i
$$339$$ 21.8038i 1.18422i
$$340$$ 0 0
$$341$$ 19.3923 + 33.5885i 1.05015 + 1.81892i
$$342$$ 1.90192 3.29423i 0.102844 0.178131i
$$343$$ −10.0000 + 15.5885i −0.539949 + 0.841698i
$$344$$ −2.76795 1.59808i −0.149238 0.0861625i
$$345$$ 4.39230i 0.236474i
$$346$$ 8.19615i 0.440628i
$$347$$ 21.2487i 1.14069i −0.821405 0.570345i $$-0.806809\pi$$
0.821405 0.570345i $$-0.193191\pi$$
$$348$$ 9.69615 5.59808i 0.519768 0.300088i
$$349$$ −14.1962 8.19615i −0.759903 0.438730i 0.0693582 0.997592i $$-0.477905\pi$$
−0.829261 + 0.558862i $$0.811238\pi$$
$$350$$ 1.73205 2.00000i 0.0925820 0.106904i
$$351$$ 15.5885 9.00000i 0.832050 0.480384i
$$352$$ 2.36603 + 4.09808i 0.126110 + 0.218428i
$$353$$ −0.294229 0.509619i −0.0156602 0.0271243i 0.858089 0.513501i $$-0.171652\pi$$
−0.873749 + 0.486377i $$0.838318\pi$$
$$354$$ −3.29423 1.90192i −0.175086 0.101086i
$$355$$ −4.09808 2.36603i −0.217503 0.125576i
$$356$$ −2.19615 3.80385i −0.116396 0.201604i
$$357$$ 0 0
$$358$$ −12.2942 + 21.2942i −0.649770 + 1.12543i
$$359$$ 13.6865 7.90192i 0.722348 0.417048i −0.0932685 0.995641i $$-0.529732\pi$$
0.815616 + 0.578593i $$0.196398\pi$$
$$360$$ 3.00000i 0.158114i
$$361$$ −8.69615 + 15.0622i −0.457692 + 0.792746i
$$362$$ −13.3923 −0.703884
$$363$$ −9.86603 17.0885i −0.517832 0.896911i
$$364$$ −6.00000 + 6.92820i −0.314485 + 0.363137i
$$365$$ −6.00000 + 3.46410i −0.314054 + 0.181319i
$$366$$ −11.1962 + 19.3923i −0.585232 + 1.01365i
$$367$$ −25.2846 + 14.5981i −1.31985 + 0.762013i −0.983704 0.179798i $$-0.942456\pi$$
−0.336142 + 0.941811i $$0.609122\pi$$
$$368$$ 2.19615 + 1.26795i 0.114482 + 0.0660964i
$$369$$ 13.5000 23.3827i 0.702782 1.21725i
$$370$$ 6.19615i 0.322123i
$$371$$ −18.8827 3.63397i −0.980340 0.188667i
$$372$$ 12.2942 + 7.09808i 0.637426 + 0.368018i
$$373$$ −5.09808 + 8.83013i −0.263968 + 0.457207i −0.967293 0.253662i $$-0.918365\pi$$
0.703324 + 0.710869i $$0.251698\pi$$
$$374$$ 0 0
$$375$$ 0.866025 1.50000i 0.0447214 0.0774597i
$$376$$ 9.00000i 0.464140i
$$377$$ 22.3923 1.15326
$$378$$ −4.50000 12.9904i −0.231455 0.668153i
$$379$$ −9.60770 −0.493514 −0.246757 0.969077i $$-0.579365\pi$$
−0.246757 + 0.969077i $$0.579365\pi$$
$$380$$ 1.26795i 0.0650444i
$$381$$ −9.86603 + 17.0885i −0.505452 + 0.875468i
$$382$$ 3.46410 0.177239
$$383$$ 9.69615 16.7942i 0.495450 0.858145i −0.504536 0.863391i $$-0.668336\pi$$
0.999986 + 0.00524566i $$0.00166975\pi$$
$$384$$ 1.50000 + 0.866025i 0.0765466 + 0.0441942i
$$385$$ 4.09808 + 11.8301i 0.208857 + 0.602919i
$$386$$ 13.8038i 0.702597i
$$387$$ 9.58846 0.487409
$$388$$ 7.39230 + 4.26795i 0.375287 + 0.216672i
$$389$$ 21.4019 12.3564i 1.08512 0.626495i 0.152847 0.988250i $$-0.451156\pi$$
0.932273 + 0.361755i $$0.117822\pi$$
$$390$$ −3.00000 + 5.19615i −0.151911 + 0.263117i
$$391$$ 0 0
$$392$$ 4.33013 + 5.50000i 0.218704 + 0.277792i
$$393$$ −3.80385 6.58846i −0.191879 0.332344i
$$394$$ 23.6603 1.19199
$$395$$ −7.29423 + 12.6340i −0.367012 + 0.635684i
$$396$$ −12.2942 7.09808i −0.617808 0.356692i
$$397$$ −26.4904 + 15.2942i −1.32951 + 0.767595i −0.985224 0.171268i $$-0.945214\pi$$
−0.344290 + 0.938863i $$0.611880\pi$$
$$398$$ 3.46410 6.00000i 0.173640 0.300753i
$$399$$ −1.90192 5.49038i −0.0952153 0.274863i
$$400$$ −0.500000 0.866025i −0.0250000 0.0433013i
$$401$$ 3.10770 + 1.79423i 0.155191 + 0.0895995i 0.575584 0.817742i $$-0.304775\pi$$
−0.420393 + 0.907342i $$0.638108\pi$$
$$402$$ 6.00000 + 3.46410i 0.299253 + 0.172774i
$$403$$ 14.1962 + 24.5885i 0.707161 + 1.22484i
$$404$$ 5.59808 + 9.69615i 0.278515 + 0.482402i
$$405$$ −4.50000 7.79423i −0.223607 0.387298i
$$406$$ 3.23205 16.7942i 0.160404 0.833484i
$$407$$ 25.3923 + 14.6603i 1.25865 + 0.726682i
$$408$$ 0 0
$$409$$ 10.5167i 0.520015i −0.965607 0.260008i $$-0.916275\pi$$
0.965607 0.260008i $$-0.0837251\pi$$
$$410$$ 9.00000i 0.444478i
$$411$$ 12.5885i 0.620943i
$$412$$ 10.5000 + 6.06218i 0.517298 + 0.298662i
$$413$$ −5.49038 + 1.90192i −0.270164 + 0.0935876i
$$414$$ −7.60770 −0.373898
$$415$$ −5.59808 9.69615i −0.274799 0.475965i
$$416$$ 1.73205 + 3.00000i 0.0849208 + 0.147087i
$$417$$ 38.1962i 1.87047i
$$418$$ −5.19615 3.00000i −0.254152 0.146735i
$$419$$ −5.19615 9.00000i −0.253849 0.439679i 0.710734 0.703461i $$-0.248363\pi$$
−0.964582 + 0.263783i $$0.915030\pi$$
$$420$$ 3.46410 + 3.00000i 0.169031 + 0.146385i
$$421$$ 14.9904 25.9641i 0.730586 1.26541i −0.226046 0.974117i $$-0.572580\pi$$
0.956633 0.291296i $$-0.0940866\pi$$
$$422$$ 17.8301 10.2942i 0.867957 0.501115i
$$423$$ 13.5000 + 23.3827i 0.656392 + 1.13691i
$$424$$ −3.63397 + 6.29423i −0.176481 + 0.305675i
$$425$$ 0 0
$$426$$ 4.09808 7.09808i 0.198552 0.343903i
$$427$$ 11.1962 + 32.3205i 0.541820 + 1.56410i
$$428$$ 13.7942 7.96410i 0.666769 0.384959i
$$429$$ −14.1962 24.5885i −0.685397 1.18714i
$$430$$ −2.76795 + 1.59808i −0.133482 + 0.0770661i
$$431$$ 33.5885 + 19.3923i 1.61790 + 0.934094i 0.987463 + 0.157854i $$0.0504574\pi$$
0.630437 + 0.776241i $$0.282876\pi$$
$$432$$ −5.19615 −0.250000
$$433$$ 18.0000i 0.865025i −0.901628 0.432512i $$-0.857627\pi$$
0.901628 0.432512i $$-0.142373\pi$$
$$434$$ 20.4904 7.09808i 0.983570 0.340719i
$$435$$ 11.1962i 0.536814i
$$436$$ −3.59808 + 6.23205i −0.172317 + 0.298461i
$$437$$ −3.21539 −0.153813
$$438$$ −6.00000 10.3923i −0.286691 0.496564i
$$439$$ 29.6603i 1.41561i −0.706410 0.707803i $$-0.749686\pi$$
0.706410 0.707803i $$-0.250314\pi$$
$$440$$ 4.73205 0.225592
$$441$$ −19.5000 7.79423i −0.928571 0.371154i
$$442$$ 0 0
$$443$$ 9.00000i 0.427603i 0.976877 + 0.213801i $$0.0685846\pi$$
−0.976877 + 0.213801i $$0.931415\pi$$
$$444$$ 10.7321 0.509321
$$445$$ −4.39230 −0.208215
$$446$$ −6.86603 + 11.8923i −0.325116 + 0.563117i
$$447$$ 18.0000 10.3923i 0.851371 0.491539i
$$448$$ 2.50000 0.866025i 0.118114 0.0409159i
$$449$$ 9.58846i 0.452507i −0.974068 0.226254i $$-0.927352\pi$$
0.974068 0.226254i $$-0.0726478\pi$$
$$450$$ 2.59808 + 1.50000i 0.122474 + 0.0707107i
$$451$$ −36.8827 21.2942i −1.73674 1.00271i
$$452$$ 10.9019 6.29423i 0.512783 0.296056i
$$453$$ 7.26795 0.341478
$$454$$ −14.1962 + 8.19615i −0.666258 + 0.384664i
$$455$$ 3.00000 + 8.66025i 0.140642 + 0.405999i
$$456$$ −2.19615 −0.102844
$$457$$ 2.39230 0.111907 0.0559537 0.998433i $$-0.482180\pi$$
0.0559537 + 0.998433i $$0.482180\pi$$
$$458$$ −7.03590 + 12.1865i −0.328766 + 0.569439i
$$459$$ 0 0
$$460$$ 2.19615 1.26795i 0.102396 0.0591184i
$$461$$ 2.59808 4.50000i 0.121004 0.209586i −0.799160 0.601119i $$-0.794722\pi$$
0.920164 + 0.391533i $$0.128055\pi$$
$$462$$ −20.4904 + 7.09808i −0.953299 + 0.330232i
$$463$$ 1.30385 + 2.25833i 0.0605949 + 0.104954i 0.894731 0.446604i $$-0.147367\pi$$
−0.834137 + 0.551558i $$0.814034\pi$$
$$464$$ −5.59808 3.23205i −0.259884 0.150044i
$$465$$ 12.2942 7.09808i 0.570131 0.329165i
$$466$$ 0.633975 + 1.09808i 0.0293683 + 0.0508674i
$$467$$ −3.40192 5.89230i −0.157422 0.272663i 0.776516 0.630097i $$-0.216985\pi$$
−0.933938 + 0.357434i $$0.883652\pi$$
$$468$$ −9.00000 5.19615i −0.416025 0.240192i
$$469$$ 10.0000 3.46410i 0.461757 0.159957i
$$470$$ −7.79423 4.50000i −0.359521 0.207570i
$$471$$ −26.4904 15.2942i −1.22061 0.704721i
$$472$$ 2.19615i 0.101086i
$$473$$ 15.1244i 0.695419i
$$474$$ −21.8827 12.6340i −1.00511 0.580298i
$$475$$ 1.09808 + 0.633975i 0.0503832 + 0.0290887i
$$476$$ 0 0
$$477$$ 21.8038i 0.998330i
$$478$$ −1.56218 2.70577i −0.0714524 0.123759i
$$479$$ −5.19615 9.00000i −0.237418 0.411220i 0.722554 0.691314i $$-0.242968\pi$$
−0.959973 + 0.280094i $$0.909635\pi$$
$$480$$ 1.50000 0.866025i 0.0684653 0.0395285i
$$481$$ 18.5885 + 10.7321i 0.847561 + 0.489339i
$$482$$ −1.66987 2.89230i −0.0760606 0.131741i
$$483$$ −7.60770 + 8.78461i −0.346162 + 0.399714i
$$484$$ −5.69615 + 9.86603i −0.258916 + 0.448456i
$$485$$ 7.39230 4.26795i 0.335667 0.193798i
$$486$$ 13.5000 7.79423i 0.612372 0.353553i
$$487$$ −17.0000 + 29.4449i −0.770344 + 1.33427i 0.167031 + 0.985952i $$0.446582\pi$$
−0.937375 + 0.348323i $$0.886751\pi$$
$$488$$ 12.9282 0.585232
$$489$$ 14.5359 0.657336
$$490$$ 6.92820 1.00000i 0.312984 0.0451754i
$$491$$ −23.4904 + 13.5622i −1.06011 + 0.612053i −0.925462 0.378841i $$-0.876323\pi$$
−0.134644 + 0.990894i $$0.542989\pi$$
$$492$$ −15.5885 −0.702782
$$493$$ 0 0
$$494$$ −3.80385 2.19615i −0.171143 0.0988096i
$$495$$ −12.2942 + 7.09808i −0.552584 + 0.319035i
$$496$$ 8.19615i 0.368018i
$$497$$ −4.09808 11.8301i −0.183824 0.530654i
$$498$$ 16.7942 9.69615i 0.752567 0.434495i
$$499$$ 8.09808 14.0263i 0.362520 0.627903i −0.625855 0.779939i $$-0.715250\pi$$
0.988375 + 0.152037i $$0.0485832\pi$$
$$500$$ −1.00000 −0.0447214
$$501$$ −18.0000 −0.804181
$$502$$ 18.0000i 0.803379i
$$503$$ 7.39230 0.329607 0.164803 0.986326i $$-0.447301\pi$$
0.164803 + 0.986326i $$0.447301\pi$$
$$504$$ −5.19615 + 6.00000i −0.231455 + 0.267261i
$$505$$ 11.1962 0.498222
$$506$$ 12.0000i 0.533465i
$$507$$ 0.866025 + 1.50000i 0.0384615 + 0.0666173i
$$508$$ 11.3923 0.505452
$$509$$ 4.79423 8.30385i 0.212500 0.368062i −0.739996 0.672611i $$-0.765173\pi$$
0.952496 + 0.304550i $$0.0985060\pi$$
$$510$$ 0 0
$$511$$ −18.0000 3.46410i −0.796273 0.153243i
$$512$$ 1.00000i 0.0441942i
$$513$$ 5.70577 3.29423i 0.251916 0.145444i
$$514$$ −24.5885 14.1962i −1.08455 0.626165i
$$515$$ 10.5000 6.06218i 0.462685 0.267131i
$$516$$ −2.76795 4.79423i −0.121852 0.211054i
$$517$$ 36.8827 21.2942i 1.62210 0.936519i
$$518$$ 10.7321 12.3923i 0.471539 0.544487i
$$519$$ 7.09808 12.2942i 0.311571 0.539657i
$$520$$ 3.46410 0.151911
$$521$$ −10.5000 + 18.1865i −0.460013 + 0.796766i −0.998961 0.0455727i $$-0.985489\pi$$
0.538948 + 0.842339i $$0.318822\pi$$
$$522$$ 19.3923 0.848778
$$523$$ 28.5788 16.5000i 1.24967 0.721495i 0.278623 0.960401i $$-0.410122\pi$$
0.971043 + 0.238906i $$0.0767888\pi$$
$$524$$ −2.19615 + 3.80385i −0.0959394 + 0.166172i
$$525$$ 4.33013 1.50000i 0.188982 0.0654654i
$$526$$ 6.86603 + 11.8923i 0.299373 + 0.518529i
$$527$$ 0 0
$$528$$ 8.19615i 0.356692i
$$529$$ −8.28461 14.3494i −0.360200 0.623885i
$$530$$ 3.63397 + 6.29423i 0.157850 + 0.273404i
$$531$$ −3.29423 5.70577i −0.142957 0.247609i
$$532$$ −2.19615 + 2.53590i −0.0952153 + 0.109945i
$$533$$ −27.0000 15.5885i −1.16950 0.675211i
$$534$$ 7.60770i 0.329217i
$$535$$ 15.9282i 0.688636i
$$536$$ 4.00000i 0.172774i
$$537$$ −36.8827 + 21.2942i −1.59161 + 0.918914i
$$538$$ 15.5885 + 9.00000i 0.672066 + 0.388018i
$$539$$ −12.2942 + 30.7583i −0.529550 + 1.32486i
$$540$$ −2.59808 + 4.50000i −0.111803 + 0.193649i
$$541$$ −4.00000 6.92820i −0.171973 0.297867i 0.767136 0.641484i $$-0.221681\pi$$
−0.939110 + 0.343617i $$0.888348\pi$$
$$542$$ −3.29423 5.70577i −0.141499 0.245084i
$$543$$ −20.0885 11.5981i −0.862078 0.497721i
$$544$$ 0 0
$$545$$ 3.59808 + 6.23205i 0.154125 + 0.266952i
$$546$$ −15.0000 + 5.19615i −0.641941 + 0.222375i
$$547$$ −2.79423 + 4.83975i −0.119473 + 0.206933i −0.919559 0.392952i $$-0.871454\pi$$
0.800086 + 0.599885i $$0.204787\pi$$
$$548$$ −6.29423 + 3.63397i −0.268876 + 0.155236i
$$549$$ −33.5885 + 19.3923i −1.43352 + 0.827643i
$$550$$ 2.36603 4.09808i 0.100888 0.174743i
$$551$$ 8.19615 0.349168
$$552$$ 2.19615 + 3.80385i 0.0934745 + 0.161903i
$$553$$ −36.4711 + 12.6340i −1.55091 + 0.537251i
$$554$$ 20.9545 12.0981i 0.890271 0.513998i
$$555$$ 5.36603 9.29423i 0.227775 0.394518i
$$556$$ 19.0981 11.0263i 0.809939 0.467618i
$$557$$ −28.3923 16.3923i −1.20302 0.694564i −0.241795 0.970327i $$-0.577736\pi$$
−0.961226 + 0.275763i $$0.911069\pi$$
$$558$$ 12.2942 + 21.2942i 0.520456 + 0.901457i
$$559$$ 11.0718i 0.468287i
$$560$$ 0.500000 2.59808i 0.0211289 0.109789i
$$561$$ 0 0
$$562$$ 7.33013 12.6962i 0.309203 0.535555i
$$563$$ −13.6077 −0.573496 −0.286748 0.958006i $$-0.592574\pi$$
−0.286748 + 0.958006i $$0.592574\pi$$
$$564$$ 7.79423 13.5000i 0.328196 0.568453i
$$565$$ 12.5885i 0.529600i
$$566$$ −16.8564 −0.708528
$$567$$ 4.50000 23.3827i 0.188982 0.981981i
$$568$$ −4.73205 −0.198552
$$569$$ 6.00000i 0.251533i −0.992060 0.125767i $$-0.959861\pi$$
0.992060 0.125767i $$-0.0401390\pi$$
$$570$$ −1.09808 + 1.90192i −0.0459934 + 0.0796628i
$$571$$ 21.6077 0.904254 0.452127 0.891954i $$-0.350665\pi$$
0.452127 + 0.891954i $$0.350665\pi$$
$$572$$ −8.19615 + 14.1962i −0.342698 + 0.593571i
$$573$$ 5.19615 + 3.00000i 0.217072 + 0.125327i
$$574$$ −15.5885 + 18.0000i −0.650650 + 0.751305i
$$575$$ 2.53590i 0.105754i
$$576$$ 1.50000 + 2.59808i 0.0625000 + 0.108253i
$$577$$ 20.7846 + 12.0000i 0.865275 + 0.499567i 0.865775 0.500433i $$-0.166826\pi$$
−0.000500448 1.00000i $$0.500159\pi$$
$$578$$ 14.7224 8.50000i 0.612372 0.353553i
$$579$$ 11.9545 20.7058i 0.496811 0.860502i
$$580$$ −5.59808 + 3.23205i −0.232447 + 0.134204i
$$581$$ 5.59808 29.0885i 0.232247 1.20679i
$$582$$ 7.39230 + 12.8038i 0.306421 + 0.530737i
$$583$$ −34.3923 −1.42438
$$584$$ −3.46410 + 6.00000i −0.143346 + 0.248282i
$$585$$ −9.00000 + 5.19615i −0.372104 + 0.214834i
$$586$$ 14.1962 8.19615i 0.586438 0.338580i
$$587$$ −15.4019 + 26.6769i −0.635705 + 1.10107i 0.350660 + 0.936503i $$0.385957\pi$$
−0.986365 + 0.164571i $$0.947376\pi$$
$$588$$ 1.73205 + 12.0000i 0.0714286 + 0.494872i
$$589$$ 5.19615 + 9.00000i 0.214104 + 0.370839i
$$590$$ 1.90192 + 1.09808i 0.0783010 + 0.0452071i
$$591$$ 35.4904 + 20.4904i 1.45988 + 0.842862i
$$592$$ −3.09808 5.36603i −0.127330 0.220542i
$$593$$ 13.3923 + 23.1962i 0.549956 + 0.952552i 0.998277 + 0.0586791i $$0.0186889\pi$$
−0.448321 + 0.893873i $$0.647978\pi$$
$$594$$ −12.2942 21.2942i −0.504438 0.873713i
$$595$$ 0 0
$$596$$ −10.3923 6.00000i −0.425685 0.245770i
$$597$$ 10.3923 6.00000i 0.425329 0.245564i
$$598$$ 8.78461i 0.359229i
$$599$$ 4.39230i 0.179465i −0.995966 0.0897324i $$-0.971399\pi$$
0.995966 0.0897324i $$-0.0286012\pi$$
$$600$$ 1.73205i 0.0707107i
$$601$$ −27.5885 15.9282i −1.12536 0.649725i −0.182594 0.983188i $$-0.558449\pi$$
−0.942763 + 0.333464i $$0.891783\pi$$
$$602$$ −8.30385 1.59808i −0.338440 0.0651327i
$$603$$ 6.00000 + 10.3923i 0.244339 + 0.423207i
$$604$$ −2.09808 3.63397i −0.0853695 0.147864i
$$605$$ 5.69615 + 9.86603i 0.231582 + 0.401111i
$$606$$ 19.3923i 0.787759i
$$607$$ −5.30385 3.06218i −0.215277 0.124290i 0.388485 0.921455i $$-0.372999\pi$$
−0.603761 + 0.797165i $$0.706332\pi$$
$$608$$ 0.633975 + 1.09808i 0.0257111 + 0.0445329i
$$609$$ 19.3923 22.3923i 0.785816 0.907382i
$$610$$ 6.46410 11.1962i 0.261724 0.453319i
$$611$$ 27.0000 15.5885i 1.09230 0.630641i
$$612$$ 0 0
$$613$$ 3.39230 5.87564i 0.137014 0.237315i −0.789351 0.613942i $$-0.789583\pi$$
0.926365 + 0.376627i $$0.122916\pi$$
$$614$$ 23.7846 0.959869
$$615$$ −7.79423 + 13.5000i −0.314294 + 0.544373i
$$616$$ 9.46410 + 8.19615i 0.381320 + 0.330232i
$$617$$ 15.8038 9.12436i 0.636239 0.367333i −0.146925 0.989148i $$-0.546938\pi$$
0.783164 + 0.621815i $$0.213604\pi$$
$$618$$ 10.5000 + 18.1865i 0.422372 + 0.731570i
$$619$$ 14.1962 8.19615i 0.570592 0.329431i −0.186794 0.982399i $$-0.559810\pi$$
0.757386 + 0.652968i $$0.226476\pi$$
$$620$$ −7.09808 4.09808i −0.285066 0.164583i
$$621$$ −11.4115 6.58846i −0.457929 0.264386i
$$622$$ 15.8038i 0.633677i
$$623$$ −8.78461 7.60770i −0.351948 0.304796i
$$624$$ 6.00000i 0.240192i
$$625$$ −0.500000 + 0.866025i −0.0200000 + 0.0346410i
$$626$$ 20.1962 0.807201
$$627$$ −5.19615 9.00000i −0.207514 0.359425i
$$628$$ 17.6603i 0.704721i
$$629$$ 0 0
$$630$$ 2.59808 + 7.50000i 0.103510 + 0.298807i
$$631$$ 12.3923 0.493330 0.246665 0.969101i $$-0.420665\pi$$
0.246665 + 0.969101i $$0.420665\pi$$
$$632$$ 14.5885i 0.580298i
$$633$$ 35.6603 1.41737
$$634$$ 20.5359 0.815585
$$635$$ 5.69615 9.86603i 0.226045 0.391521i
$$636$$ −10.9019 + 6.29423i −0.432289 + 0.249582i
$$637$$ −9.00000 + 22.5167i −0.356593 + 0.892143i
$$638$$ 30.5885i 1.21101i
$$639$$ 12.2942 7.09808i 0.486352 0.280796i
$$640$$ −0.866025 0.500000i −0.0342327 0.0197642i
$$641$$ 2.78461 1.60770i 0.109985 0.0635001i −0.443998 0.896028i $$-0.646440\pi$$
0.553984 + 0.832528i $$0.313107\pi$$
$$642$$ 27.5885 1.08883
$$643$$ −16.2058 + 9.35641i −0.639093 + 0.368981i −0.784265 0.620426i $$-0.786960\pi$$
0.145172 + 0.989406i $$0.453626\pi$$
$$644$$ 6.58846 + 1.26795i 0.259622 + 0.0499642i
$$645$$ −5.53590 −0.217976
$$646$$ 0 0
$$647$$ −2.30385 + 3.99038i −0.0905736 + 0.156878i −0.907753 0.419506i $$-0.862203\pi$$
0.817179 + 0.576384i $$0.195537\pi$$
$$648$$ −7.79423 4.50000i −0.306186 0.176777i
$$649$$ −9.00000 + 5.19615i −0.353281 + 0.203967i
$$650$$ 1.73205 3.00000i 0.0679366 0.117670i
$$651$$ 36.8827 + 7.09808i 1.44555 + 0.278196i
$$652$$ −4.19615 7.26795i −0.164334 0.284635i
$$653$$ −43.1769 24.9282i −1.68964 0.975516i −0.954786 0.297294i $$-0.903916\pi$$
−0.734857 0.678222i $$-0.762751\pi$$
$$654$$ −10.7942 + 6.23205i −0.422088 + 0.243692i
$$655$$ 2.19615 + 3.80385i 0.0858108 + 0.148629i
$$656$$ 4.50000 + 7.79423i 0.175695 + 0.304314i
$$657$$ 20.7846i 0.810885i
$$658$$ −7.79423 22.5000i −0.303851 0.877141i
$$659$$ −33.2942 19.2224i −1.29696 0.748800i −0.317081 0.948398i $$-0.602703\pi$$
−0.979878 + 0.199599i $$0.936036\pi$$
$$660$$ 7.09808 + 4.09808i 0.276292 + 0.159517i
$$661$$ 13.1436i 0.511227i 0.966779 + 0.255613i $$0.0822774\pi$$
−0.966779 + 0.255613i $$0.917723\pi$$
$$662$$ 8.00000i 0.310929i
$$663$$ 0 0
$$664$$ −9.69615 5.59808i −0.376284 0.217247i
$$665$$ 1.09808 + 3.16987i 0.0425816 + 0.122922i
$$666$$ 16.0981 + 9.29423i 0.623788 + 0.360144i
$$667$$ −8.19615 14.1962i −0.317356 0.549677i
$$668$$ 5.19615 + 9.00000i 0.201045 + 0.348220i
$$669$$ −20.5981 + 11.8923i −0.796368 + 0.459783i
$$670$$ −3.46410 2.00000i −0.133830 0.0772667i
$$671$$ 30.5885 + 52.9808i 1.18085 + 2.04530i
$$672$$ 4.50000 + 0.866025i 0.173591 + 0.0334077i
$$673$$ 12.4904 21.6340i 0.481469 0.833928i −0.518305 0.855196i $$-0.673437\pi$$
0.999774 + 0.0212674i $$0.00677013\pi$$
$$674$$ −8.66025 + 5.00000i −0.333581 + 0.192593i
$$675$$ 2.59808 + 4.50000i 0.100000 + 0.173205i
$$676$$ 0.500000 0.866025i 0.0192308 0.0333087i
$$677$$ 22.9808 0.883222 0.441611 0.897207i $$-0.354407\pi$$
0.441611 + 0.897207i $$0.354407\pi$$
$$678$$ 21.8038 0.837372
$$679$$ 22.1769 + 4.26795i 0.851072 + 0.163789i
$$680$$ 0 0
$$681$$ −28.3923 −1.08800
$$682$$ 33.5885 19.3923i 1.28617 0.742570i
$$683$$ −30.7750 17.7679i −1.17757 0.679872i −0.222121 0.975019i $$-0.571298\pi$$
−0.955452 + 0.295148i $$0.904631\pi$$
$$684$$ −3.29423 1.90192i −0.125958 0.0727219i
$$685$$ 7.26795i 0.277694i
$$686$$ 15.5885 + 10.0000i 0.595170 + 0.381802i
$$687$$ −21.1077 + 12.1865i −0.805309 + 0.464945i
$$688$$ −1.59808 + 2.76795i −0.0609261 + 0.105527i
$$689$$ −25.1769 −0.959164
$$690$$ 4.39230 0.167212
$$691$$ 5.07180i 0.192940i 0.995336 + 0.0964701i $$0.0307552\pi$$
−0.995336 + 0.0964701i $$0.969245\pi$$
$$692$$ −8.19615 −0.311571
$$693$$ −36.8827 7.09808i −1.40106 0.269634i
$$694$$ −21.2487 −0.806590
$$695$$ 22.0526i 0.836501i
$$696$$ −5.59808 9.69615i −0.212195 0.367532i
$$697$$ 0 0
$$698$$ −8.19615 + 14.1962i −0.310229 + 0.537332i
$$699$$ 2.19615i 0.0830661i
$$700$$ −2.00000 1.73205i −0.0755929 0.0654654i
$$701$$ 44.3205i 1.67396i −0.547232 0.836981i $$-0.684318\pi$$
0.547232 0.836981i $$-0.315682\pi$$
$$702$$ −9.00000 15.5885i −0.339683 0.588348i
$$703$$ 6.80385 + 3.92820i 0.256612 + 0.148155i
$$704$$ 4.09808 2.36603i 0.154452 0.0891729i
$$705$$ −7.79423 13.5000i −0.293548 0.508439i
$$706$$ −0.509619 + 0.294229i −0.0191798 + 0.0110734i
$$707$$ 22.3923 + 19.3923i 0.842149 + 0.729323i
$$708$$ −1.90192 + 3.29423i −0.0714787 + 0.123805i
$$709$$ −46.7846 −1.75703 −0.878516 0.477712i $$-0.841466\pi$$
−0.878516 + 0.477712i $$0.841466\pi$$
$$710$$ −2.36603 + 4.09808i −0.0887954 + 0.153798i
$$711$$ −21.8827 37.9019i −0.820665 1.42143i
$$712$$ −3.80385 + 2.19615i −0.142555 + 0.0823043i
$$713$$ 10.3923 18.0000i 0.389195 0.674105i
$$714$$ 0 0
$$715$$ 8.19615 + 14.1962i 0.306519 + 0.530906i
$$716$$ 21.2942 + 12.2942i 0.795803 + 0.459457i
$$717$$ 5.41154i 0.202098i
$$718$$ −7.90192 13.6865i −0.294897 0.510777i
$$719$$ −20.7846 36.0000i −0.775135 1.34257i −0.934718 0.355389i $$-0.884348\pi$$
0.159583 0.987184i $$-0.448985\pi$$
$$720$$ 3.00000 0.111803
$$721$$ 31.5000 + 6.06218i 1.17312 + 0.225767i
$$722$$ 15.0622 + 8.69615i 0.560556 + 0.323637i
$$723$$ 5.78461i 0.215132i
$$724$$ 13.3923i 0.497721i
$$725$$ 6.46410i 0.240071i
$$726$$ −17.0885 + 9.86603i −0.634212 + 0.366163i
$$727$$ 41.7846 + 24.1244i 1.54971 + 0.894723i 0.998164 + 0.0605756i $$0.0192936\pi$$
0.551542 + 0.834147i $$0.314040\pi$$
$$728$$ 6.92820 + 6.00000i 0.256776 + 0.222375i
$$729$$ 27.0000 1.00000
$$730$$ 3.46410 + 6.00000i 0.128212 + 0.222070i
$$731$$ 0 0
$$732$$ 19.3923 + 11.1962i 0.716760 + 0.413822i
$$733$$ −29.4904 17.0263i −1.08925 0.628880i −0.155875 0.987777i $$-0.549820\pi$$
−0.933377 + 0.358897i $$0.883153\pi$$
$$734$$ 14.5981 + 25.2846i 0.538825 + 0.933272i
$$735$$ 11.2583 + 4.50000i 0.415270 + 0.165985i
$$736$$ 1.26795 2.19615i 0.0467372 0.0809513i
$$737$$ 16.3923 9.46410i 0.603818 0.348615i
$$738$$ −23.3827 13.5000i −0.860729 0.496942i
$$739$$ −16.5885 + 28.7321i −0.610216 + 1.05693i 0.380987 + 0.924580i $$0.375584\pi$$
−0.991204 + 0.132345i $$0.957749\pi$$
$$740$$ −6.19615 −0.227775
$$741$$ −3.80385 6.58846i −0.139738 0.242033i
$$742$$ −3.63397 + 18.8827i −0.133407 + 0.693205i
$$743$$ −23.6769 + 13.6699i −0.868622 + 0.501499i −0.866890 0.498499i $$-0.833885\pi$$
−0.00173176 + 0.999999i $$0.500551\pi$$
$$744$$ 7.09808 12.2942i 0.260228 0.450728i
$$745$$ −10.3923 + 6.00000i −0.380745 + 0.219823i
$$746$$ 8.83013 + 5.09808i 0.323294 + 0.186654i
$$747$$ 33.5885 1.22894
$$748$$ 0 0
$$749$$ 27.5885 31.8564i 1.00806 1.16401i
$$750$$ −1.50000 0.866025i −0.0547723 0.0316228i
$$751$$ 10.8038 18.7128i 0.394238 0.682840i −0.598766 0.800924i $$-0.704342\pi$$
0.993004 + 0.118084i $$0.0376752\pi$$
$$752$$ −9.00000 −0.328196
$$753$$ 15.5885 27.0000i 0.568075 0.983935i
$$754$$ 22.3923i 0.815480i
$$755$$ −4.19615 −0.152714
$$756$$ −12.9904 + 4.50000i −0.472456 + 0.163663i
$$757$$ −8.58846 −0.312153 −0.156076 0.987745i $$-0.549885\pi$$
−0.156076 + 0.987745i $$0.549885\pi$$
$$758$$ 9.60770i 0.348967i
$$759$$ −10.3923 + 18.0000i −0.377217 + 0.653359i
$$760$$ 1.26795 0.0459934
$$761$$ −16.5000 + 28.5788i −0.598125 + 1.03598i 0.394973 + 0.918693i $$0.370754\pi$$
−0.993098 + 0.117289i $$0.962579\pi$$
$$762$$ 17.0885 + 9.86603i 0.619049 + 0.357408i
$$763$$ −3.59808 + 18.6962i −0.130259 + 0.676846i
$$764$$ 3.46410i 0.125327i
$$765$$ 0 0
$$766$$ −16.7942 9.69615i −0.606800 0.350336i
$$767$$ −6.58846 + 3.80385i −0.237895 + 0.137349i
$$768$$ 0.866025 1.50000i 0.0312500 0.0541266i
$$769$$ −13.5000 + 7.79423i −0.486822 + 0.281067i −0.723255 0.690581i $$-0.757355\pi$$
0.236433 + 0.971648i $$0.424022\pi$$
$$770$$ 11.8301 4.09808i 0.426328 0.147684i
$$771$$ −24.5885 42.5885i −0.885532 1.53379i
$$772$$ −13.8038 −0.496811
$$773$$ 9.00000 15.5885i 0.323708 0.560678i −0.657542 0.753418i $$-0.728404\pi$$
0.981250 + 0.192740i $$0.0617373\pi$$
$$774$$ 9.58846i 0.344650i
$$775$$ −7.09808 + 4.09808i −0.254970 + 0.147207i
$$776$$ 4.26795 7.39230i 0.153210 0.265368i
$$777$$ 26.8301 9.29423i 0.962525 0.333429i
$$778$$ −12.3564 21.4019i −0.442999 0.767296i
$$779$$ −9.88269 5.70577i −0.354084 0.204430i
$$780$$ 5.19615 + 3.00000i 0.186052 + 0.107417i
$$781$$ −11.1962 19.3923i −0.400630 0.693911i
$$782$$ 0 0
$$783$$ 29.0885 + 16.7942i 1.03954 + 0.600177i
$$784$$ 5.50000 4.33013i 0.196429 0.154647i
$$785$$ 15.2942 + 8.83013i 0.545874 + 0.315161i